पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४७२

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276 GANITASARAGANGRAHA drawn which will extend from north to eouth. 'The straight line running through the middle of the angles of this (fish-shaped figure) represents of itself the northern and the southern direct tions. The intermediate directions have to be ascertained as boing derivable from half the (interspace between these) directions 4. The (measure of the) equinoctial shadow is indeed half of the sum of the measures of the shadows obtained at the middle of the day-time (or noon) on days when the sun enters the sign of Aries as also the sign of Libra. 5ई. In Laika, Yavakoti, Siddhapuri, and Romakनpuri, there is no (such) equinoctial shadow at all; and, therefore, the day-time is of 80 ghat08. 6. In other regionE, the day-time happens to be longer or shorter by 80 ghatas. On the days of the entrance (of the sum) into Aries and into Libra, the day-time is everywhere of 80 ghata (in duration). 7ी. Having understood the measure of the duration of the day time and also of the shadow at (noom or) the middle of the day according to the way described in astronomyone should learn herein the calculations regarding shadows by means of the collec tion of rules hereafter to be given. The rule for arriving at the time of day, on knowing the measure of the shadow of a given style at a given time (in the foronoon or afternoon ) in relation to a place where there is no equinoctial shadow: 84. One is added to the measure of the shadow (expressed in terms of the height of an object), and (the sum so resulting) &y. If u be the height of the object and a the length of its shadow hen the time of the day that has elapsed or has to elapse is, according to the rule given here, equal to_4_ , where A is the angle repre 2 (cot. A + 1) + 1) senting the altitude of the ann at the time. It may be seen that this formula gives only the approximate value of the time of the day in all caees except when the altitude is 45', and that the approximation is very rough only in the case of large altitudes, nearing 90°. The formula seems to be based on the fact that for Emal values the angles in a right-angled triangle are approximately proportional to the opposite sides